A set of multiuser beamforming, or multiuser multiple-input and multiple-output (MU-MIMO), schemes has been actively discussed in the wireless standards including 3GPP LTE/LTE-A and IEEE 802.16m \cite{3gppmimo,16m_web,16m_emd,16m_sdd,16m_cfp,16m_base}. Although the high-rate feedback signaling is required for accurate transmit processing, multiuser beamforming can offer significant system throughput enhancement compared to conventional single user multistream beamforming, or single user MIMO (SU-MIMO), schemes even when a single receiver antenna is equipped at each UE \cite{foschini1996, Telatar1999, alamouti1998, Tarokh99, Hochwald2002submit, Visawanath02, Goldsmith03, Knopp1995, Chung03, Heath2001Nov, Chung2001}. Per-User Unitary Rate Control (PU$^2$RC) is the cellular network initiation of multiuser beamforming, which effectively utilizes both multiuser precoding and scheduling to enhance the system performance of multiple antenna cellular standards \cite{PU2RC_PTO,sjkim06,PU2RC_HSDPA,PU2RC_LTE,sjkim2004pimrc}. PU$^2$RC uses the feedback information codebook consisting of $2^{B-\log_2 M}$ unitary matrices where $2^B$ is the number of total precoding vectors in the codebook and $M$ is the number of transmit antennas \cite{love2003}. After each UE feeds back the preferred matrix index (PMI), the relative preferred vector index (PVI) in the selected preferred matrix and the channel quality information based on the PMI and PVI information to the BS, the BS selects maximum throughput users for each PVI and the best PMI based on the selected users so as to transmit multiple streams for multiple users.

While the channel quality information for user $m$ in the PU$^2$RC system is given by

$ \mathrm{CQI}_{\mathrm{MU},m} = \frac{\frac{\mathrm{SNR}}{M} |\mathbf{h}_m^H \mathbf{w}_m|^2} {1+\frac{\mathrm{SNR}}{M} \sum_{l \neq M} |\mathbf{h}_m^H \mathbf{w}_l|^2} = \frac{||\mathbf{h}_m||^2 \cos^2( \angle \mathbf{h}_m, \mathbf{w}_m)} {\frac{M}{\mathrm{SNR}} + \sum_{l \neq M} ||\mathbf{h}_m||^2 \cos^2( \angle \mathbf{h}_m, \mathbf{w}_l)} \geq \frac{||\mathbf{h}_m||^2 \cos^2( \angle \mathbf{h}_m, \mathbf{w}_m)} {\frac{M}{\mathrm{SNR}} + ||\mathbf{h}_m||^2 (1 - \cos^2( \angle \mathbf{h}_m, \mathbf{w}_m))} $

where $\mathbf{h}_m$ is the channel vector and $\mathbf{w}_m$ is the beamforming vector, the original single user single stream beamforming system feeds back \begin{eqnarray} \mathrm{CQI}_{\mathrm{SU},m} = \mathrm{SNR} |\mathbf{h}_m^H \mathbf{w}_m|^2. \end{eqnarray} The multiuser scheduling scheme in multiuser multi-stream beamforming systems can operated with $\mathrm{CQI}_{\mathrm{SU},m}$, which results in rare spatial multiuser diversity gain. To switch single user and multiuser beamforming modes without significant overhead, the PU$^2$RC scheme is evolved to the dynamic switch scheme which allows to variate the mode according to the channel and scheduling condition. The feedback load for the dynamic scheme is reduced by sending back $\mathrm{CQI}_{\mathrm{SU},m}$ using general amount of the feedback bits and $\Delta \mathrm{CQI}_{\mathrm{MU},m} = \mathrm{CQI}_{\mathrm{SU},m} - \mathrm{CQI}_{\mathrm{MU},m}$ using small amount of the feedback bits.


If the number of unitary matrices in the codebook becomes large, it becomes not easy to find users who share the same unitary matrix because the precision of channel quantization is increased. To adapt the larger codebook size, the unitary rotating strategy is proposed in \cite{WLee08}. Alternative scheme to the unitary ration is ZF beamforming which is a linear suboptimal solution of dirty paper coding, where DPC has been proved to achieve both the sum-rate and multiuser capacity region of the MIMO broadcast channels \cite{Sharif2004, Caire2003Jul, Costa1983, Vishwanath2003Oct, Yu2002June, Viswanath2003Aug, Weingarten2004March}. Both the unitary rotation and the ZF beamforming require the additional introduction of the dedicated pilot signals, leading to generating new burdensome for downlink data transmission \cite{Caire07s}. It is noteworthy that all the aforementioned multiuser beamforming approaches discussing in wireless cellular standards are based on the unitary preferred scheduling and the feedback codebook mechanism, which are principle techniques proposed in PU$^2$RC \cite{Ravindran09}.

The next generation wireless local area network (WLAN) standards are also considering to adopt beamforming techniques \cite{11_web}. For the 5GHz-band approach in IEEE 802.11ac, simple multiuser beamforming schemes are emerging to reduce necessary mobile terminal physical antennas and spatial processing complexity subject to the system throughput being equal to or or larger than the earlier WLAN standard (IEEE 802.11n) and for the 60GHz-band approach in IEEE 802.11ad, the analog beamforming scheme has a high probability to be adopted as the mandatory feature so that the network coverage can be extended more than that of the wireless personal area network (WPAN) systems \cite{Alalusi05}. In short, the various research activities on single user, multi-user and analog beamforming techniques are issued and debated in technical literature and wireless standards in terms of mostly simplex (uni-directional link) throughput performance improvement \cite{3gppmimo, lucent2001, ericsson2004, love2001, ong2002}.